<title>Partially compensated speckle imaging: Fourier phase spectrum estimation</title>

Abstract

Predetection compensation combined with post detection image processing for the case of imaging through atmospheric turbulence is addressed. Full and partial predetection compensation using adaptive optics is combined with bispectrum speckle imaging post-processing, and performance improvements are assessed. Full compensation was found to provide a large improvement in the signalto- noise ratio (SNR) of the power spectrum estimate compared to the uncompensated case. Lower degrees of correction provided smaller improvements in the power spectrum SNR, and a very low degree of compensation provided results indistinguishable from the uncompensated case. Three regions of performance improvement were found with respect to the object Fourier phase spectrum estimate: 1) the fully compensated case, where bispectrum post processing provided no improvement in the phase estimate over that obtained from a fully compensated long exposure image; 2) a partially compensated regime, where applying bispectrum post processing to the compensated images provided phase spectrum estimation superior to the uncompensated bispectrum case; and 3) a very poorly compensated regime, where the results were essentially indistinguishable from the uncompensated case. Previously validated simulation codes were used to conduct this investigation.